One-stage cluster sample: every element of each sampled cluster

The variance depends on the spread of the cluster means and not at all on the spread within a cluster. The design effect against simple random sampling of the same number of elements is returned.

Usage

Clus1(Y, M = Inf, level = 0.95)

Arguments

Y

Sampled clusters, one row per cluster, all of size k.

M

Number of clusters in the population; Inf if unknown.

level

Confidence level.

Value

List with estimate, se, ci_lower, ci_upper, cluster_mean, between_var, within_var, deff, rho, m, k.

Details

Formula: ybar_c = (1/m) sum_i ybar_i; v(ybar_c) = (1 - m/M) s_b^2 / m, s_b^2 = sum (ybar_i - ybar_c)^2 / (m - 1)

References

Cochran (1977), Sampling Techniques, 3rd edition, Chapter 9. Chapter 9 was NOT in the scanned excerpt available to this batch, so the standard published form is used; the finite-population factor (M - m)/M matches the convention of the sibling Cochran modules.

Examples

V <- c(1, 2, 3, 4, 5, 6, 7, 8)
Clus1(V)
#> $estimate
#> [1] 4.5
#> 
#> $se
#> [1] 0.8660254
#> 
#> $ci_lower
#> [1] 2.802621
#> 
#> $ci_upper
#> [1] 6.197379
#> 
#> $cluster_mean
#> [1] 1 2 3 4 5 6 7 8
#> 
#> $between_var
#> [1] 6
#> 
#> $within_var
#> [1] 0
#> 
#> $deff
#> [1] 1
#> 
#> $rho
#> [1] NaN
#> 
#> $m
#> [1] 8
#> 
#> $k
#> [1] 1
#> 
#> $method
#> [1] "One-stage cluster sampling, equal cluster sizes"
#> 
#> attr(,"class")
#> [1] "morie_rich_result" "list"